Biomedical Engineering Reference
In-Depth Information
quantum mechanical calculations with large quantum numbers. A plot of ψ
30
(Figure 11.3)
shows the operation of the correspondence principle; the probabilities appear much more
evenly spread out over the region. In the case of a 'classical' particle in such a well, we
would expect an equal probability of finding the particle at any point along the line.
2
1.5
1
0.5
0
0.2
0.4
0.6
0.8
1
x
/L
Figure 11.3
Square of wavefunction n
=
30
11.5 Two-Dimensional Infinite Well
In the two-dimensional version of this problem, we consider a single particle of mass
m
constrained to a region of the
xy
plane by a potential that is infinite everywhere except for
a region where 0
where it is equal to a constant
U
0
, as shown in
Figure 11.4. I have taken the region to be square, but this is not necessary.
≤
x
≤∞
,0
≤
y
≤∞
U
infinite
y
=
L
U
constant
y
=
0
x
=
0
x
=
L
Figure 11.4
Two-dimensional infinite well
